The younger Clinton says her mother, who was Trump's Democratic opponent in 2016 — isn't focused on politics either. Instead, she said, Hillary Clinton is writing a book and spending time with Chelsea's two young children.

When asked whether a run for office is inevitable because her parents were both politicians, Chelsea Clinton would only say that everyone should be willing to fight for programs and policies they believe in. She said, "I hope that politics is in all of our DNA."

"Right now, the answer is no," she continued. "But I think we all need to be asking ourselves that question periodically. And I hope that a lot of young people kind of use the election to think, 'Wow, like, should I run for public office? Am I the right person for a given job?' Whether it's for a school board or a senator."